Excerpt from

L.Kleine-Horst: Empiristic theory of visual
gestalt perception. Hierarchy and interactions of visual functions. (ETVG),
Part 5, III 5

**Some formative effects
of the coordinate factors**

Several well-known "geometric-optical illusions" are to be accounted for by the formative effect of the R-factor. One of them is the "Poggendorf illusion" (Fig. 5-8A). Objectively, the diagonal line on the right of the two parallel lines is collinear to the diagonal line on the left. There is, however, no collinearity to be seen. This is a formative effect of the gestalt function R+: the angle between two connected lines appears more perpendicular than it "is". As Fig. 5-8B shows, the obtuse angels are seen to be smaller, the acute angles larger than they are. In every day life, this distortion usually goes unnoticed, as the perceiver has no way of measuring it. It is only when unexpected effects arise, as a result of the phenomenal change in angle, or when the possibility of direct comparison exists, that the distortion is noticed: for example, by holding a page level with the line of sight and looking along the tilted lines.

**Figure 5-8.** Poggendorff illusion

In the "Hering illusion" (Fig. 5-9), an "objectively" straight line becomes a phenomenal arc. This is due to the intersections of the straight lines with the bundle of ray-like lines; an arc (exaggerated in B) tends to intersect the rays in angles that are more "perpendicular" than the objective angles.

**Figure 5-9.** Hering illusion

The many short parallel lines crossing one long vertical line, as in the "Zöllner illusion" (Fig. 5-10), cause the vertical line to appear somewhat tilted, i.e. the angles between the short lines and the long line appear more perpendicular than they objectively are. One would scarcely recognize this slant, if the crossing pattern was given only once. As there are, however, several such patterns, and the short lines crossing adjacent long lines are oriented perpendicularly to one another, each of the two immediately adjacent long lines are caused to be inclined in opposite directions. The resulting deviation from their objectively given parallelism is salient. A more detailed analysis of this illusion would have to consider further influence factors. According to the ETVG, the deviation from parallelism must decrease with a decreasing number (Q) of crossing short lines. But it must increase when the pattern is rotated so that the short lines take on vertical (V) and horizontal (H) orientations. In this case, the large number of short lines that are in "prägnant" orientations force the few long lines they intersect to change their own orientations.

**Figure 5-10.** Zöllner illusion Figure **Figure
5-11.** Perspective distorion

Although we have not yet treated depth perception, we shall now cite several examples of compelling three-dimensional impressions resulting from the formative effects of the gestalt factors we have already dealt with; indeed, the projection of an object onto the retina affects only the receptors whose location values are defined by the physical factor Zl. Thus the direction in space in which the light source is located is determined. The location values provide, however, no information about how distant in space the light source is. Thus, depth experience is not necessarily bound on the retinal image; depth allows itself the freedom to appear anywhere. It can thus contribute to the realization of the formative tendency of any gestalt factor. In the sensory pattern of Fig. 5-11, there is neither (seen objectively) a single right angle nor the three long lines parallel to one another. Nevertheless, a "section of railway track" is compellingly seen here, in which the rails are parallel and in which the ties meet the rails at right angles. The ties also appear to be of equal length, although, in the drawing, they are all of different lengths. All of this is possible because the section of track is perceived to extend "far into the distance". It is odd that, given such a dramatic distortion of the actual metric relationships, one speaks of the "perspective" of a drawing rather than of the "illusion". In this example, the formative effects of the gestalt functions R+, R- and M are operational.

The "Necker cube" (Fig. 5-12), likewise named after its inventor, has been known and marveled at for over 150 years as an "ambiguous figure", or a "reversal figure" (Part 2), and is recurringly the object of psychological investigation. Instead of an irregular hexagon with seven (Q7) inner fields of various shapes and sizes, we have one solid with a single (Q1) infield, an "in-space". This three-dimensional infield is in turn bordered off by six beautiful squares against the outfield ("out-space"). Thus the Necker cube does not only satisfy the "demands" of the form factors R, M and S of lines and edges; it satisfies the demands also of "simplicity", the opposite of "complexity", as the perception of the stimulus pattern, as a three-dimensional object, "disentangles" the functional hierarchy (Part 6).

**Figure 5-12**. Necker cube Figure **5-13.**
Kite or bed sheet?

To conclude with, there is a nice example of the additional formative effect of the gestalt factor "straightness" in Fig. 5-13 (from Bühler, 1913). The pattern can be interpreted as a two-dimensional object, such as a "kite" with four bent edges; it is more saliently interpreted as straight-edged rectangular bed sheet on a washing line, being "inflated" by the wind into the third dimension.

The R-factor (with its two functions R+ and R-) is the "highest factor" of the basic factor hierarchy. Its actualization requires the actualization of all its lower factors: the lower form factors, the orientation factors, and the quantity factor (at the value 4). These functional connections are the reason the factors form a unity. If one constructs a pattern that contains the gestalt stimuli for the normative effect of all these factors mentioned one receives the full coordinate system, from which Fig. 5-14 is an extract, as the full system is extended infinitely in the vertical and horizontal directions, and with an infinite number of subdivisions. It consists in a grating of two infinite quantities (Q) of parallel (R-), straight (S) and widthless extensions (E), at equal spatial intervals from one another (M), that cross at right angles (R+), and that are oriented (T) horizontally (H) and vertically (V). When focused (Zl=0) on any crossing, the orientations are physico-functionally differentiated into directions to the left (Zhl), to the right (Zhr), upward (Zvu), and downward (Zvd). This grating is well-known, and called the Cartesian coordinate cross.

**Figure 5-14**. Cartesian coordinate cross

Every high-level visual phenomenon, formed by multiple encapsulating actualization of the factor hierarchy, underlies more or less the constraints of this (in Fig. 5-14 phenomenalized) functional coordinate system, or the factors it constitutes from, respectively. One can understand the specific formative effects of the figure factors (at Levels 1 to 5) as an "overshooting" copy of relationships often existing naturally. The formative effects of the orientation and form factors, however, lead to an experience of relationships which are practically non-existent naturally, for example, rectangularity, straightness, and parallelism. There are only a few exceptions: in living beings, bilateral symmetry of the body is wide-spread, which is characterized in that the body ends on the left and on the right in equal (M) right-angled (R+) distance from an (abstract, i.e. functionally existent) straight (S) line (E), designated the "symmetry axis".

I must admit: there are still several uncertainties, at least in respect to both the hierarchical order and the normative effect of the quantity, orientation, and form factors. Experimental research is needed to diminish them.